Periodic solutions and refractory periods in the soliton theory for nerves and the locust femoral nerve

TL;DR

This paper explores how soliton theory can explain periodic nerve pulse generation and refractory periods, aligning theoretical predictions with experimental observations in locust nerves near melting transitions.

Contribution

It introduces a theoretical framework for periodic solutions in nerve pulse propagation, incorporating boundary conditions that produce refractory periods and hyperpolarization effects.

Findings

Periodic pulse solutions can be derived from the wave equation under nerve length conservation.

The theory explains the occurrence of minimum-distance doublet pulses in locust nerves.

Comparison shows good agreement between theoretical pulses and experimental nerve action potentials.

Abstract

Close to melting transitions it is possible to propagate solitary electromechanical pulses which reflect many of the experimental features of the nerve pulse including mechanical dislocations and reversible heat production. Here we show that one also obtains the possibility of periodic pulse generation when the boundary condition for the nerve is the conservation of the overall length of the nerve. This condition generates an undershoot beneath the baseline (`hyperpolarization') and a `refractory period', i.e., a minimum distance between pulses. In this paper, we outline the theory for periodic solutions to the wave equation and compare these results to action potentials from the femoral nerve of the locust (locusta migratoria). In particular, we describe the frequently occurring minimum-distance doublet pulses seen in these neurons and compare them to the periodic pulse solutions.